List of Examples

IV.1.1 Semi-standard deviation and second order LPM
IV.1.2 LPM risk metrics
IV.1.3 Probability of underperforming a benchmark
IV.1.4 VaR with normally distributed returns
IV.1.5 Scaling normal VaR with independent and with autocorrelated returns
IV.1.6 Adjusting VaR for non-zero expected excess returns
IV.1.7 Equity VaR
IV.1.8 Normal VaR of a simple cash flow
IV.1.9 Benchmark VaR with normally distributed returns
IV.1.10 Comparison of different VaR metrics
IV.1.11 Non-sub-additivity of VaR
IV.2.1 Adjusting normal linear VaR for autocorrelation
IV.2.2 Converting a covariance matrix to basis points
IV.2.3 Normal linear VaR from a mapped cash flow
IV.2.4 Incremental VaR for a cash flow
IV.2.5 Normal linear VaR for an exposure to two yield curves
IV.2.6 Spread and LIBOR components of normal linear VaR
IV.2.7 Applying a cash-flow map to interest rate scenarios
IV.2.8 VaR of UK fixed income portfolio
IV.2.9 Using principal components as risk factors
IV.2.10 Computing the PC VaR
IV.2.11 VaR for cash equity positions
IV.2.12 Systematic VaR based on an equity factor model
IV.2.13 Disaggregation of VaR into systematic VaR and specific VaR
IV.2.14 Equity and forex VaR
IV.2.15 VaR for international equity exposures
IV.2.16 Interest rate VaR from forex exposure
IV.2.17 VaR for a hedged international stock portfolio
IV.2.18 Estimating student t linear VaR at the portfolio level
IV.2.19 Comparison of normal and student t linear VaR
IV.2.20 Estimating normal mixture VaR for equity and forex
IV.2.21 Comparison of normal mixture and student t linear VaR
IV.2.22 Comparison of normal mixture and Student t mixture VaR
IV.2.23 Mixture VaR in the presence of autocorrelated returns
IV.2.24 Normal mixture VaR – risk factor level
IV.2.25 EWMA normal linear VaR for FTSE 100
IV.2.26 Comparison of RiskMetrics™ regulatory and EWMA VaR
IV.2.27 Normal ETL
IV.2.28 Student t distributed ETL
IV.2.29 Normal mixture ETL
IV.2.30 Student t mixture ETL
IV.3.1 Volatility adjusted VaR for the S&P 500 index
IV.3.2 Filtered historical simulation VaR for the S&P 500 index
IV.3.3 Using the GPD to estimate VaR at extreme quantiles
IV.3.4 Cornish–Fisher expansion
IV.3.5 Johnson SU VaR
IV.3.6 Volatility-adjusting historical VaR for a stock portfolio
IV.3.7 Systematic and specific components of historical VaR
IV.4.1 Linear congruential random number generation
IV.4.2 Discrepancy of linear congruential generators
IV.4.3 Antithetic variance reduction
IV.4.4 Stratified sampling from standard uniform distributions
IV.4.5 Latin hypercube sampling
IV.4.6 Multi-step Monte Carlo with EWMA volatility
IV.4.7 Multi-step Monte Carlo with asymmetric GARCH volatility
IV.4.8 Multivariate normal Monte Carlo VaR
IV.4.9 Multivariate Student t Monte Carlo VaR
IV.4.10 Monte Carlo VaR based on copulas
IV.4.11 Monte Carlo credit spread VaR
IV.4.12 Monte Carlo interest rate VaR with PCA
IV.4.13 Monte Carlo VaR with normal mixture distributions
IV.4.14 VaR with volatility and correlation clustering
IV.5.1 Delta–Normal VaR
IV.5.2 Delta–gamma VaR with Johnson distribution
IV.5.3 Static and dynamic historical VaR for an option
IV.5.4 Historical VaR and ETL of a delta-hedged option
IV.5.5 Interest rate, price and volatility risks of options
IV.5.6 VaR and ETL for a delta–gamma–vega hedged portfolio
IV.5.7 Historical VaR with Greeks approximation
IV.5.8 Historical VaR for options on several underlyings
IV.5.9 Historical VaR for a path-dependent option
IV.5.10 Monte Carlo VaR for a standard European option
IV.5.11 Non-linear, non-normal Monte Carlo VaR
IV.5.12 Gamma, vega and theta effects in short term VaR
IV.5.13 Theta effects in long-term VaR
IV.5.14 One-step versus multi-step Monte Carlo VaR
IV.5.15 GARCH Monte Carlo VaR for options
IV.5.16 Monte Carlo VaR for a path-dependent option
IV.5.17 Monte Carlo VaR of strangle: exact revaluation
IV.5.18 Monte Carlo VaR with delta–gamma–vega mapping
IV.5.19 Monte Carlo VaR with multivariate delta–gamma mapping
IV.5.20 Monte Carlo VaR with multivariate delta– gamma–vega mapping
IV.6.1 Model risk arising from cash-flow map
IV.6.2 Model risk arising from equity beta estimation
IV.6.3 Confidence intervals for normal linear VaR
IV.6.4 Confidence intervals for quantiles
IV.6.5 Unconditional coverage test
IV.6.6 Independence test
IV.6.7 Regression-based backtest
IV.6.8 Coverage tests with volatility clustering
IV.6.9 Backtesting ETL
IV.6.10 Bias test on normal linear VaR
IV.6.11 Likelihood ratio backtest of normal risk models
IV.6.12 A dynamic distribution backtest
IV.7.1 Historical worst case and distribution scenarios
IV.7.2 Hypothetical distribution scenario: bank insolvency
IV.7.3 Scenario based VaR for unlisted securities
IV.7.4 Scenario interest rate and credit spread VaR
IV.7.5 Scenario based VaR for commodity futures
IV.7.6 Scenario VaR with a small probability of a market crash
IV.7.7 Credit spread normal mixture scenario VaR
IV.7.8 Comparison of Bayesian VaR and scenario VaR
IV.7.9 A factor push stress test
IV.7.10 Worst case loss in specified trust region
IV.7.11 Covariance matrix from global equity crash of 1987
IV.7.12 Stressed historical VaR
IV.7.13 Finding the ‘nearest’ correlation matrix
IV.7.14 Principal component stress tests
IV.7.15 Stressed VaR with exogenous illiquidity
IV.7.16 Stressed VaR with endogenous liquidity
IV.7.17 Adjusting VaR for price-quantity impact
IV.7.18 Using FHS for stress testing
IV.7.19 Using GARCH with Monte Carlo for stress testing
IV.8.1 Calculating GRC for a long-only position using VaR
IV.8.2 Comparison of internal and standardized MRC for a hedged position
IV.8.3 MRC and economic capital
IV.8.4 Aggregation of economic capital
IV.8.5 Simple illustration of aggregation risk
IV.8.6 Calculating RORAC
IV.8.7 Aggregating RORAC
IV.8.8 Comparing RAROC for swaps and bonds
IV.8.9 Maximizing RAROC for optimal capital allocation
IV.8.10 Constrained economic capital allocation
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